Energy dispersive X-ray analysis is frequently used to determine the composition of electron transparent specimens in electron beam instruments. Early techniques for determining composition included ratio techniques based on pure bulk samples and standard composition samples that could be used to convert X-ray intensities into elemental compositions. These approaches avoided the need to know in detail the X-ray detector efficiency, but consequently required standard samples for each element and accelerating voltage used. Pure, elemental thin film specimens have been used in a ratio technique to calibrate an X-ray detector for each element and operating voltage. These techniques and others in which the composition or determination is calculated from theoretical values without using standards have suffered from significant uncertainties associated with the X-ray detector. It has been proposed that the effects of the X-ray detector can be accounted for by determining a detector efficiency function (DEF) using standard alloy specimens. See, e.g., the article by N. J. Zaluzec in Introduction to Analytical Electron Microscopy, Plenum Press, New York (1979). The DEF is typically expressed as the relative X-ray detection efficiency of the X-ray detector as a function of X-ray photon energy. Once a DEF is determined for an instrument, the instrument is effectively calibrated for determining the composition of all elements and at all operating conditions. One approach proposed for determining the DEF is a technique using thin film specimens of pure materials to determine the detector efficiency at several discrete X-ray energies. See W. E. King; Symposium on High-Resolution Electron Microscopy, Tempe, AZ, Jan. 7-11, 1985.
The quantification of X-ray signals in electron microscopes to determine specimen composition requires the conversion of X-ray signal intensity from each element in a sample into a weight fraction for the sample. Because the efficiencies of production and detection of X-rays differ for each element in the sample, the ratio of signal intensities of two elements does not equal the ratio of their composition. For thin-film analysis, the ratio of intensities I.sub.a and I.sub.b for two elements (elements "a" and "b") can be related to the ratio of the composition of the elements, C.sub.a and C.sub.b, by a constant, i.e., C.sub.a /C.sub.b =K.sub.ab I.sub.a /I.sub.b, where K.sub.ab is experimentally determined. This equation forms the basis of the ratio technique for quantification of X-ray signals. To use this technique, K.sub.ab must be determined experimentally by the use of composition "standards". This approach, while quite reliable, is limited because alloy samples of known composition must be prepared for each element that is to be analyzed. It is sometimes difficult or impossible to prepare homogeneous samples for this purpose. Given the availability of suitable samples, the instrument must be calibrated for each element of interest. Furthermore, since the constant K.sub.ab is a function of the energy of the electrons, it must be determined for each accelerating voltage of the instrument.
Another approach to quantification handles the effects of X-ray production and X-ray detection separately. In this approach, the basis of quantification is the equation: C.sub.a /C.sub.b =K.sub.b .epsilon..sub.b I.sub.a /K.sub.a .epsilon..sub.a I.sub.b, where K.sub.a and K.sub.b are the X-ray generation constants for elements a and b and .epsilon..sub.a and .epsilon..sub.b is the efficiency of detection for X-ray photons from elements a and b. Because of its greater generality, this latter formulation of the ratio has been recognized as a preferable approach to quantification. The X-ray generation constants are dependent on the sample and the accelerating voltage and are reasonably well-known. However, it is difficult to be able to determine the efficiency of detection .epsilon..sub.a and .epsilon..sub.b for all elements. The theoretical form of the X-ray detector efficiency function is known, and thus a continuous detector efficiency function (DEF) could possibly be used, which would allow calculation of the values of the detector efficiency at the X-ray photon energies characteristically emitted by the elements a and b. However, because of the large uncertainties in some of the important parameters in this theoretical function (primarily with regard to the detector window thickness and dead layer thickness), outright theoretical calculation of the detector efficiencies .epsilon..sub.a and .epsilon..sub.b does not appear to be a satisfactory approach.
Several experimental techniques have been devised to determine the detector efficiency function, but these techniques have not found routine application. For example, experimental determinations of the detector efficiency at a particular X-ray energy can be made on samples of known composition. If pure materials are used as samples (elements or stoichiometric compounds), then any uncertainties in the nature of the composition are eliminated. However, the electron path length through the material must be known accurately to obtain accurate efficiency values. For thin foils used as samples in the transmission electron microscope, several samples of various materials must be made and examined in the microscope, and the sample thickness must be measured with accuracy for each sample. The time consuming and difficult task of analyzing several samples to obtain a one time calibration for any one instrument has been an impediment to the routine determination of detector efficiency functions.